Problem: The grades on a physics midterm at Springer are normally distributed with $\mu = 81$ and $\sigma = 3.0$. Gabriela earned a $76$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{76 - {81}}{{3.0}}} $ ${ z \approx -1.67}$ The z-score is $-1.67$. In other words, Gabriela's score was $1.67$ standard deviations below the mean.